The Time Wheel is an ancient device that was designed to move the Island to a different location in space and time if its existence should ever be threatened by the outside world.
The Time Wheel is a wooden wheel with eight large spokes that is partially embedded in the wall of a frozen underground chamber on the Island. It is connected to an unseen mechanism behind the wall that, when turned, manipulates the electromagnetic energy at the core of the Island to move it through time and space to a new location on Earth. In regards to the Time Wheel, Ben Linus said "push it to the right, we end up in the future, push it to the left, we end up in the past", and "one rung is... 5 years, give or take", but there does not appear to be a more accurate way to control the date and location that the Island would be moved to. However, this does not rule out the possibility that such a method could exist if the Island's energy was manipulated by a device that was sufficiently more advanced than the Time Wheel.
When the Time Wheel is turned and the Island is moved, the entire chamber is bathed in electromagnetic radiation that transports the operator of the wheel to the "exit point" of the Island: a location in the Tunisian desert. It is not known why this happens, but the inhabitants of the Island seem to view turning the wheel as some kind of cosmic punishment because whoever turns the wheel is teleported off the Island and can "never come back", because the Island would have been moved to a different era and location in their absence. Of course, this would not prevent banished time travellers from returning to the island if they knew where and when it was.
Quolas was inside the Time Wheel chamber when he was first discovered by the inhabitants of the Island. The Islanders concluded that Quolas was a hostile entity who had come to exploit the Source of the Island and attacked him, but Quolas escaped and became a consistent thorn in their side by disappearing and moving to a different location on the Island whenever he was discovered.
In 150,084 CMT, the Islanders found Quolas again inside a temple on the Island, except this time, Quolas was accompanied by four other aliens: Kakamu, Nadle, D-Klak, and Bob. Nadle's claim that "someone is going to erase our timelines, and [The Island] is instrumental in stopping him", made Ben Linus think that the aliens were after the Time Wheel. Ben demanded to know how Nadle knew about the Time Wheel, but to his surprise, Nadle did not, so Ben negotiated a ceasefire and led the aliens into a room to discuss why they were really there. Ben told the aliens that the Time Wheel was a "wheel that moves [the Islanders] through time", but refused to elaborate even after D-Klak warned him about Mazkertis, because he did not believe that time could be changed. In response, Quolas gave Ben a practical demonstration of how time could be changed by taking him back in time to meet his younger self and cut off one of Past Ben's toes. Quolas then brought Present Ben back to the present, where he found that he was now also missing a toe, and apparently had been ever since that day in the new, altered timeline. This forced Ben to accept that the threat posed by Mazkertis was real, so he decided that the Time Wheel must be used to move the Island to a different era to minimize the chances of Mazkertis finding or harming the Island.
Ben wrote a note addressed to Kaira and told Tomas to deliver it to her, then informed the aliens of the need to move the Island with the Time Wheel, which would banish whoever used it from the Island. D-Klak volunteered to turn the Time Wheel because he would have no need to return to the Island when banished, so Ben guided D-Klak to the Time Wheel and gave him a brief explanation of how to operate it. D-Klak turned the wheel and the Island was transported to another location and time period on Earth while D-Klak was teleported to present-day Tunisia.